So, you catch a 'thief'...

And you know all that for a fact?

Suppose I yanked someone's bag and ran off clutching a few hundred quid in folding beer tokens? Would that be a non-emergency crime?

Methinks I need a change of career...

yes i know that for a fact, and your second contrived point would be classed as an emergency if it just happened not if it happened 2 hours ago.

let's leave it there shall we